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∑k=1504(4k−1)(20154k−1) \large\displaystyle \sum_{k=1}^{504} \left ( 4k-1 \right ) \binom{2015}{4k-1} k=1∑504(4k−1)(4k−12015)
If the sum above can be written as p.qr p.q^{r} p.qr, where ppp, qqq and rrr are positive integers with qqq being a prime.
Evaluate p+q+r p+q+r p+q+r.
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